Actually, there is a "fourth" type of conditional sentence called "Mixed Conditionals."

YES, you can put together in one sentence type 2 and type 3 conditionals to express an unreal past with results in the present.

Other examples:
If George had attended the meeting (last week), he would be aware of the latest developments (now).
If costs hadn't gone up twenty percent, we would be making a profit.
If you had received the press release, you would know about the product.

For more details, you can check "The Oxford Dictionary of English Grammar." (Conditional, p. 84)